The father of a slain North Carolina woman pleaded with the killer to come forward Friday, calling the murder an "act of extreme cowardice."

His plea came a day after explosive allegations that the young mother's husband was having an affair and she felt trapped in the U.S. were released in court documents filed by the family of 34-year-old Nancy Cooper.

Garry Rentz, along with his wife, Donna, and Nancy's twin sister, Khrista Lister, claimed Nancy's husband Bradley Cooper was having an affair when she was murdered and kept her from returning to her native Canada, according to an emergency custody petition filed Wednesday.

"This is an act of extreme cowardice by whoever did this, and I think if they have a shred of decency in their body, they would come forward and admit their guilt," Garry Rentz said at a press conference Friday about the investigation into his daughter's death.

A custody hearing is scheduled for July 25, according to The News & Observer of Raleigh.

The family said a candlelight memorial will be held Friday evening and a memorial service was planned Saturday afternoon in Cary, N.C. A Canadian service will take place next Wednesday in Edmonton, Alberta.

At a press conference Friday, officials refused to answer questions about the status of the investigation on the advice of the Wake County District Attorney's Office.

"Everyone continues to be cooperative with us, and I am pleased with the progress that we are making at this time,” Cary, N.C., Police Chief Patricia Bazemore said.

Bazemore said she is confident that the case will be brought to an "appropriate conclusion." There will be no more news conferences until detectives make an arrest in Nancy Cooper's murder, she said.

The Rentzes, Nancy's brother and her brother-in-law spoke with the press Friday about their grandchildren, Isabella ("Bella"), 4, and Gabriella ("Katie"), who will turn 2 later this month.

The grandparents and twin sister were granted temporary custody Wednesday by a North Carolina court after filing the emergency petition in which they allege Brad Cooper, 34, posed a threat "to the physical safety of the children."

"Our primary concern is the care of these children," Donna Rentz said Friday, adding later: "You can be assured that we're going to take very good care of them."

The complaint, characterized by investigators as a private matter, also alleges that Nancy Cooper, a Canadian citizen, was desperate to return to Canada with her two American-born daughters. The family accuses Brad Cooper of hiding the two children's passports so they could not leave the country.

The family moved to North Carolina when Brad, who works for Cisco Systems, accepted a transfer from Calgary. The company secured Brad Cooper a temporary work visa; Nancy Cooper's was attached to his.

"I want to stress that this custody issue is a private civil matter between Nancy’s family and Brad. It was not initiated by the Town of Cary Police Department, and it was not a part of our investigation into Nancy’s murder," Bazemore said Thursday. "That said, any information that comes from this civil matter will be considered by investigators as we move forward in this case."

The family declined to comment on the custody issue again Friday.

But in court papers, Nancy Cooper's family said she'd recently hired a lawyer to deal with potential separation from her husband and custody issues.

The custody change came as Brad Cooper's attorney issued a statement late Wednesday saying the young father will continue to assist authorities in "bringing the killer or killers to justice" in his wife's murder investigation.

"Brad is devastated by the news of Nancy's death," the statement read. "To avoid jeopardizing the investigation, he will not be answering any questions from the press."

Bazemore said Thursday that investigators are continuing their search, a day after warrants were served on the Coopers' house and two vehicles. Six bags of evidence were taken from the Lochmere subdivision home on Wednesday afternoon, and a judge ordered Brad Cooper to submit blood and saliva samples for DNA testing.

"Investigations are as much about ruling things out as about ruling things in," Bazemore said. "We have still not named a suspect or a person of interest. Everyone in this case continues to be cooperative with us."

Authorities launched a murder investigation Tuesday after Nancy's body was found in a Wake County cul-de-sac, near where her husband said she'd gone jogging.

The mother of two small girls went for a routine run at about 7 a.m. Saturday morning but did not come home by 9 a.m. to meet friends, as had been the plan, her husband said.

Nancy Cooper's parents do not believe she went running, according to court papers. They said Brad Cooper was the last person to see her alive.

Medical examiners confirmed the identity of the body found the previous evening by a man walking his dog miles from Cooper’s home, Bazemore said.

A friend of Nancy Cooper reported her missing at 2:15 p.m. Saturday when she did not show up for a get-together. Police said they didn't know why her husband wasn't the one to alert authorities that his wife had disappeared.